A laboratory balance uses a uniform beam XY XY\,XY of length 0.6 m which is pivoted at its center. To calibrate the scale, a circular silicon wafer with a diameter of 120 mm and a mass of 80 g is placed on the beam.
The wafer is positioned such that its edge is perfectly aligned with end XXX. A calibration weight of mass M gramsM \text{ grams}M grams is suspended from the other end of the beam at Y Y\,Y using a light inextensible string.
Given that the beam is in equilibrium in a horizontal position, determine the value of MMM.
State an assumption made about the silicon wafer to perform this calculation.
53 exam-style questions on OCR A Level Maths 3.4 Moments (A-level only), covering 3.4.1 Moment of a force (A-level only), 3.4.2 Equilibrium of a rigid body (A-level only), and 3.4.3 Moments in static contexts (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.